HARD LEVEL · OFFICIAL STYLE
ACT Math
Core Concepts & Practice
20 exam-style multiple choice questions · Detailed explanations · Real ACT difficulty
Algebra & Functions
Linear, quadratic, systems, functions, and inequalities.
ax² + bx + c = 0
x = (-b ± √(b²-4ac)) / 2a
x = (-b ± √(b²-4ac)) / 2a
Geometry
Triangles, circles, area, volume, and coordinate geometry.
A = πr² · V = (4/3)πr³
a²+b²=c² (Pythagorean)
a²+b²=c² (Pythagorean)
Trigonometry
SOH-CAH-TOA, unit circle, trig identities.
sin²θ + cos²θ = 1
tan θ = sin θ / cos θ
tan θ = sin θ / cos θ
Statistics & Prob.
Mean, median, probability, data interpretation.
P(A∪B) = P(A)+P(B)-P(A∩B)
Mean = Σx / n
Mean = Σx / n
KEY FORMULAS TO MEMORIZE
Slope: m = (y₂-y₁)/(x₂-x₁)
Distance: d = √((x₂-x₁)²+(y₂-y₁)²)
Arc length = (θ/360) × 2πr
30-60-90: 1 : √3 : 2
45-45-90: 1 : 1 : √2
log_b(x) + log_b(y) = log_b(xy)
Cylinder V = πr²h
Cone V = (1/3)πr²h
SAMPLE QUESTION — EXAMPLE
If f(x) = 2x² − 3x + 1, what is the value of f(−2)?
✓ Answer: f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15
HARD
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Answer Key & Full Explanations
Complete solutions for all 20 questions